Apparatus and method for synchronizing frequency in orthogonal frequency division multiplexing communication system

ABSTRACT

A frequency synchronization apparatus for an orthogonal frequency division multiplexing (OFDM) communication system includes a radio frequency (RF) receiving module for receiving OFDM signal, an analog/digital (A/D) converter connected to the RF receiving module, the A/D converter converting the OFDM signal into a digital signal, a frequency synchronization module connected to the A/D converter, the frequency synchronization module synchronizing carrier frequency, a Fast Fourier Transformer (FFT) connected to the frequency synchronization module, the FFT performing fast Fourier transformation to symbols from the frequency synchronization module, a channel estimation module connected to the FFT, the channel estimation module estimating channel response, an equalizer connected to the FFT and the channel estimation module, the equalizer equalizing channel, a residual phase tracking module connected to the equalizer, the residual phase tracking module tracking residual phase, a demodulator connected to the residual phase tracking module, the demodulator demodulating, and a controller connected to the frequency synchronization module, the controller controlling the frequency synchronization module.

BACKGROUND OF THE INVENTION

(a) Field of the Invention

The present invention relates to an apparatus and method for frequencysynchronization, and in particular, to an apparatus and method forcompletely synchronizing carrier frequency through a digital process inan orthogonal frequency division multiplexing (OFDM) wirelesscommunication system.

(b) Description of the Related Art

In OFDM, original data stream is multiplexed into N parallel datastreams each of the data streams modulated with a different frequencyusing an Inverse Fast Fourier Transform (IFFT), and the resultingsignals are transmitted together in the same band.

The OFDM symbols are artificially prolonged by periodically repeating aguard interval which is longer than a maximum channel delay so as toremove the reflections of previous symbols, which preserves theorthogonality such that inter symbol interferences (ISI) and interchannel interference are reduced.

Successful OFDM reception requires that a receiver maintains correctsymbol synchronization which means that the receiver knows at whichpoint of time each symbol begins and ends.

Maintaining the symbol synchronization is difficult if a transmitter andreceiver are moving with respect to each other. For example, if a mobilestation moves around in an urban environment, the propagation path ofthe signal changes constantly, resulting in attenuation and reflection.Also, the mobile station moving fast causes phase jitter and Dopplershift, resulting in frequency offset which means difference in frequencybetween the transmitter and receiver. This frequency offset causes intersymbol interference and damages the orthogonality condition requiredamong the subcarriers, resulting in degradation of bit error rate.

Accordingly, in order for the receiver to be able to successfullyreceive the symbols, the receiver has to synchronize carrier frequencybetween the transmitter and receiver before performing the Fast FourierTransform (FFT).

To reduce the carrier frequency offset, a wireless modem adopting theOFDM modulation sends a training signal for channel estimation andinitial frequency synchronization. The Wireless Local Area Networkstandards such as the HIPERLAN/2 developed by the EuropeanTelecommunications Standards Institute (ETSI) and the 802.11a of theInstitute of Electrical and Electronics Engineers (IEEE) specify a shorttraining sequence in which 16 samples are repeated 10 times and a longtraining sequence in which 64 time samples are repeated twice.

In the conventional synchronization method, the frequencysynchronization device estimates the carrier frequency offsets using thetraining signals in digital domain and passes the signals through a loopfilter so as to control a voltage controlled oscillator (VCO) such thatthe VCO output is used to synchronize the carrier frequency in analogdomain.

In other cases, especially for single carrier transmission, a numericalcontrolled oscillator (NCO) is used for compensating the frequencyoffset in the digital domain.

However, in the carrier frequency synchronization method of theconventional OFDM system in which the carrier frequency synchronizationis performed in analog domain, it is impossible to perform a precisecarrier frequency synchronization since the carrier frequencysynchronization is performed using the output of the VCO that iscontrolled by the signal generated by the estimated frequency offsetsand this causes the synchronization time delay.

Also, in the conventional method, since the carrier frequency offset isestimated in digital domain and the frequency offset is compensatedusing the VCO in analog domain, its implementation and performanceanalysis are difficult in this mixed analog-digital mode.

As the implementation method for obtaining an arctangent and exponentialfunction for synchronizing carrier frequency in digital domain, thetechniques employing the Coordinate Rotation Digital Computer (CORDIC)and Look-up table are used.

However, the CORDIC method has a drawback in that the computing speed isslow and the precision is low despite of its simple implementation. Onthe other hand, the look-up table method requires lots of memory modulescausing a hardware complexity and it is difficult to create addresses inlook-up table in spite of its fast speed and high precision.

SUMMARY OF THE INVENTION

The present invention has been made in an effort to solve the aboveproblems of the prior art.

It is an object of the present invention to provide a frequencysynchronization apparatus and method for the orthogonal frequencydivision multiplexing (OFDM) communication system capable ofsynchronizing carrier frequency while maintaining a high precision ofdata reception regardless of the time delay by compensating frequencyoffsets in the digital domain.

It is another object of the present invention to provide a frequencysynchronization apparatus and method for the OFDM communication systemcapable of precisely estimating the frequency offset in a broadestimation range using a coarse and fine modes.

It is another object of the present invention to provide a frequencysynchronization apparatus and method for the OFDM communication systemcapable of tracking a residual phase by implementing the same hardwareused in the coarse and fine mode estimation circuits so as to share inparts.

It is still another object of the present invention to provide afrequency synchronization apparatus and method for the OFDMcommunication system capable of performing computation with a highprecision in simple hardware using a look-up table containing arctangentand log functions required for estimating and compensating the frequencyoffset.

To achieve the above objects, the frequency synchronization apparatusfor an orthogonal frequency division multiplexing (OFDM) communicationsystem according to the present invention comprises, a radio frequency(RF) receiving module for receiving OFDM signal, an analog/digital (A/D)converter connected to the RF receiving module, the A/D converterconverting the OFDM signal into a digital signal, a frequencysynchronization module connected to the A/D converter, a Fast FourierTransformer (FFT) connected to the frequency synchronization module, achannel estimation module connected to the FFT, an equalizer connectedto the FFT and the channel estimation module, a residual phase trackingmodule connected to the equalizer, a demodulator connected to theresidual phase tracking module, and a controller connected to thefrequency synchronization module.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute apart of the specification, illustrate an embodiment of the invention,and together with the description, serve to explain the principles ofthe invention.

FIG. 1 a is a block diagram showing a frequency synchronizationapparatus in the orthogonal frequency division multiplexing (OFDM)communication system according to a preferred embodiment of the presentinvention;

FIG. 1 b is a block diagram showing a frequency synchronization moduleof the frequency offset synchronization apparatus of FIG. 1 a;

FIG. 1 c is a block diagram showing a residual phase tracking module ofthe frequency synchronization apparatus of FIG. 1 a;

FIG. 1 d is a block diagram illustrating the operation of the frequencysynchronization part of FIG. 1 b when using a single training signal;

FIG. 1 e is a block diagram illustrating the operation of the residualphase tracking module of FIG. 1 c when a pilot signal is set to apredetermined value;

FIG. 2 a is a flow chart illustrating a frequency synchronization methodof the OFDM communication system according to the referred embodiment ofthe present invention when using two training signals;

FIG. 2 b is a flow chart illustrating the frequency synchronizationmethod of the OFDM communication when using one training signal;

FIG. 3 shows a structure of the training signal according to thepreferred embodiment of the present invention;

FIG. 4 is a drawing illustrating effects of the frequency offsets and aninitial phase at the point of frequency compensation;

FIG. 5 is a drawing illustrating effects of carrier frequency offsets ofdata symbol periods;

FIG. 6 is a drawing illustrating effects of the carrier frequencyoffsets and an initial phase at the point of frequency compensation whena single step frequency offset synchronization method is used with asingle training signal;

FIG. 7 shows graphs for illustrating an implementation of an arctangenttable according to the preferred embodiment of the present invention;

FIG. 8 is a drawing for illustrating a phase adjustment method accordingto the preferred embodiment of the present invention;

FIG. 9 a pair of drawings showing the sine and cosine waveforms;

FIG. 10 is a drawing illustrating an operation of a bit expander of thefrequency synchronization apparatus of FIG. 1; and

FIG. 11 is a drawing for illustrating address generation in a sine andcosine tables in accordance with region.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

A preferred embodiment of the present invention will be describedhereinafter with reference to the accompanying drawings. A frequencysynchronization apparatus and method of the present invention will beexplained by embodying in an OFDM wireless modem.

FIG. 1 a, FIG. 1 b, and FIG. 1 c are respective block diagrams showing afrequency synchronization apparatus in the orthogonal frequency divisionmultiplexing (OFDM) communication system according to a preferredembodiment of the present invention, frequency offset synchronizationmodule of the frequency synchronization apparatus of FIG. 1 a, aresidual phase tracking module of the frequency synchronizationapparatus of FIG. 1 a. FIG. 1 d and FIG. 1 e are respective blockdiagrams illustrating the operation of the frequency synchronizationmodule of FIG. 1 b when using a single training signal, a block diagramillustrating the operation of the residual phase tracking module of FIG.1 c when a pilot signal is set to a predetermined value.

Referring to FIG. 1 a˜FIG. 1 c, the frequency synchronization apparatuscomprises a radio frequency (RF) receiving module 100 for receiving anOFDM signal transmitted by an OFDM transmitter, an A/D converter 200connected to the RF receiving module 100 for converting the OFDM signalinto a digital signal, a frequency synchronization module 300 connectedto the A/D converter 200 for synchronizing a carrier frequency, a FastFourier Transformer (FFT) 400 connected to the frequency synchronizationmodule 300 for performing the fast Fourier transformation on everysymbol therefrom, a channel estimation module 450 connected to the FFT400 for estimating channel, an equalizer 500 connected to the FFT 400, aresidual phase tracking module 600 connected to the equalizer 500 forestimating the residual phase, and a demodulator 700 connected to theresidual phase tracking module 600 for demodulating the modulated signalso as to reproduce the original signal.

The frequency synchronization module 300 comprises an estimationsubmodule 310 for estimating a frequency offset and residual phase ofthe received signal, a first demultiplexer 330 for selectivelyoutputting the frequency offset and residual phase in accordance with acontrol signal from the controller 10, an adder 340 for adding thefrequency offset from the estimation submodule, a frequency offsetcompensation submodule 320 for compensating the received signal and datasymbol using the frequency offsets from the first demultiplexer 330 theadder 340, and a second demultiplexer 350 for selectively outputting thesignal from the frequency offset compensation submodule 320 according tothe control signal from the controller 10.

The estimation submodule 310 comprises a shift register part 311 fordelaying a sample of the training signal and outputting conjugatecomplex numbers of a predetermined training signal and a followingtraining signal at the same time, and a selective estimation part 312for estimating the frequency offset of the signal from the shiftregister part 311 and a residual phase of the signal from the residualphase tracking module 600.

The selective estimation part 312 comprises a first multiplier 312-1 formultiplying the signals from the shift register part 311 or the residualphase tracking module 600, a first accumulator 312-2 for accumulatingthe samples obtained by calculation of the first conjugated complexnumber multiplier 312-1, a divider 312-3 for generating arctangent tableaddress on the basis of ratio of a real part to imaginary part of avalue accumulated at the accumulator 312-2, an arctangent table 312-4stored arctangent values sampled in a predetermined interval so as tooutput a corresponding arctangent value to the arctangent table addressgenerated by the divider, and a phase converter 312-5 for converting thearctangent value into a value of a corresponding region by referring toa sign of the accumulated value at the first accumulator 312-2 andoutputting the value as an estimated frequency offset.

It is preferred that the arctangent values are classified into values ofpredetermined regions and the values in a representative one of theregions stored as representative values in the arctangent table 312-4.

The frequency offset compensation submodule 320 comprises a bit expander321 for dividing the estimated frequency offset into samples of apredetermined size, a second accumulator for generating a first logfunction table address by accumulating frequency offset of each sampleobtained at the bit expander 321, a first region controller 323 foridentifying a sign of value at the bit expander and converting the firstlog function table address into a corresponding address value in apredetermined region and outputting the same, a first log function table324 for outputting the log function value stored by sampling in apredetermined distance in accordance with the address value outputtedfrom the first region controller 323, and a second multiplier 325 forcompensating the frequency offset by multiplying the training signal ordata symbol by the log function value outputted from the first logfunction table 324.

It is preferred that the sine and cosine values are divided intopredetermined regions and one of the region is divided by apredetermined value and stored in the first log function table 324.

The first region controller 323 outputs an address value resulting froma subtraction of a predetermined value from the output value and thenshift the present region to a next region. Also, the first regioncontroller 323 outputs the output value of the second accumulator 322using complementary operation for obtaining a sine or cosine value in asymmetric region.

The residual phase tracking module 600 estimates a residual phase usingthe selective estimation part 312 of the frequency offsetsynchronization module 300. The residual phase tracking module 600comprises a pilot extractor 610 for extracting a pilot signal from thedata symbol transformed by the Fourier Transform operation and sendingthe pilot signal to the selective estimation part 312, and a residualphase compensation part 620 for compensating the data symbol with theresidual phase of the data symbol estimated at the selective estimationpart 312.

The residual phase tracking compensation Dart 620 comprises a secondregion controller 621 for outputting a second log function table addresscorresponding to the residual phase value outputted from the firstdemultiplexer 330, a second log function table 622 for outputting apreviously stored log function value, which is obtained by sampling in apredetermined interval, corresponding to the log function table addressfrom the second region controller, and a third multiplier 623 forcompensating the residual phase by multiplying the log function valueoutputted from the second log function table 622 with the compensateddata symbol.

The sine and cosine values are divided into predetermined regions andthen one of the regions is divided by a predetermined value so as to bestored in the second table 622.

The second region controller 621 outputs an address resulting fromsubtracting a predetermined value from the output value and then shiftsthe present address region to a next address region if the output valuefrom the first demultiplexer 330 is greater than the predeterminedvalue. Also, the second region controller 621 outputs an addressobtained from the first demultiplexer 330 through a complementaryoperation for calculating the sine and cosine values in symmetry region.

FIG. 2 a and FIG. 2 b are flow charts illustrating frequencysynchronization method of the OFDM communication system respectivelywhen using two training signals and using one training signal.

Referring to FIG. 2 a, the frequency synchronization method of the OFDMcommunication system comprises the steps of (A) estimating andcompensating the frequency offset of the training signal, performing theFast Fourier Transform (FFT), and estimating a channel (S800˜S840); (B)compensating the data symbol of the received signal with the frequencyoffset estimated at step (A), performing the FFT, and then compensatingthe data symbol with the channel estimated at step (A) (S850˜S870); and(C) estimating and compensating a residual phase of thechannel-compensated data symbol (S880˜895).

The step (A) comprises the sub-steps of (A1) estimating the frequencyoffset using a short training signal and compensating a long trainingsignal with the estimated frequency offset when the received signal hasthe two kinds of training signals (S800˜S810; coarse mode), (A2)re-estimating the frequency offset of the long training signalcompensated at the sub-step A1 and re-compensating the long trainingsignal (S820˜830; fine mode).

At step (B), the data symbol is compensated by multiplying theexponential function with the frequency offsets estimated at thesub-steps (A1) and (A2), i.e., at the coarse and fine modes.

The sub-step (A1) comprises the stages of (A1-1) performing a conjugatecomplex number computation and accumulation thereof by delaying a sampleof the short training signal, creating an arctangent table address byobtaining a ratio of real and imaginary parts of the accumulated value;and (A1-2) outputting estimated frequency offset by identifying a codeof the accumulated value and transforming the arctangent value accordingto the arctangent table address to a corresponding region value; (A1-3)dividing the estimated frequency offset into predetermined sizes,accumulating them, and creating a first log function table address;(A1-4) transforming the first log function table address into acorresponding region address by identifying the accumulated code valueof the stage (A1-3) and then outputting a log function valuecorresponding to the transformed address; and (A1-5) compensating thefrequency offset by multiplying the long training signal with the logfunction value outputted at the stage (A1-4) (not shown).

The stage (A1-1) has a sub-stage of dividing the arctangent value into apredetermined regions and then dividing one of the regions by apredetermined value so as to be previously stored in the arctangenttable.

The stage (A1-4) has a sub-stage of dividing the sine and cosine valuesinto the predetermined regions and then one of the regions by apredetermined value so as to be previously stored in the first logfunction table, and outputting the sine and cosine values correspondingto the value resulting from subtracting a predetermined value from theaccumulated value and shifting the present address region to the nextregion if the accumulated value is greater than the predetermined value.

At the stage (A1-3), the address value created for obtaining the sine orcosine value of the symmetric region is outputted after thecomplementary operation.

The sub-step (A2) comprises the stages of (A2-1) creating an arctangenttable address by delaying sample of the frequency-compensated longtraining signal and performing the conjugate complex number calculationand accumulation thereof and obtaining the ratio of the real andimaginary parts of the accumulated value, (A2-2) outputting theestimated frequency offset by identifying the code of the accumulatedvalue and transforming the arctangent value of the arctangent tableaddress to the corresponding region value, (A2-3) accumulating theestimated frequency offset after dividing in the predetermined size andcreating the log function table address, (A2-4) transforming the firstlog function table address to the corresponding region address byidentifying the accumulated code value of the stage (A2-3) and thenoutputting the log function value corresponding to the transformedaddress, and (A2-5) compensating the frequency offset by multiplying thelog function value outputted at the stage (A2-4) with thefrequency-compensated long training signal of the step (A1) (not shown).

The stage (A2-1) has sub-stage of dividing the arctangent value intopredetermined regions and then dividing one of the regions by apredetermined value so as to be previously stored in the arctangenttable.

The stage (A2-4) has a sub-stage of dividing the sine and cosine valuesinto the predetermined regions and then one of the regions by apredetermined value so as to be previously stored in the first logfunction table, and outputting the sine and cosine values correspondingto the value resulting from subtracting a predetermined value from theaccumulated value and shifting the present address region to the nextregion if the accumulated value is greater than the predetermined value.

At the stage (A2-3), the address value created for obtaining the sine orcosine value of the symmetric region is outputted after thecomplementary operation.

The step (C) comprises the sub-steps of (C1) performing the conjugatecomplex number calculation and accumulation of pilot signals extractedfrom the compensated data symbols and creating arc tangent table addressby calculating the ratio of the real and imaginary parts of theaccumulated value, (C2) outputting the estimated residual phase byidentifying the code of the accumulated value and transforming thearctangent value of the arctangent table address to the correspondingregion value, (C3) creating the second log function table addressaccording to the estimated residual phase estimated at the sub-step (C2)and outputting the corresponding log function value, and (C4)compensating the residual phase by multiplying the data symbol with thelog function value outputted at the sub-step (C3).

The sub-step (C1) has a sub-stage of dividing the arctangent value intopredetermined regions and then dividing one of the regions by apredetermined value so as to previously store in the arctangent table.

The stage (C3) has a sub-stage of dividing the sine and cosine valuesinto the predetermined regions and then one of the regions by apredetermined value so as to be previously stored in the first logfunction table, and outputting the sine and cosine values correspondingto the value resulting from subtracting a predetermined value from theaccumulated value and shifting the present address region to the nextregion if the accumulated value is greater than the predetermined value.

At the stage (C3), the address value created for obtaining the sine orcosine value of the symmetric region is outputted after thecomplementary operation.

The frequency synchronization method of the present invention will bedescribed, in more detail, with reference to the FIG. 1 a˜FIG. 11hereinafter.

So far, a frequency synchronization method of synchronizing carrierfrequency offset using the short and long training signals is describedin two-step full digital approach. The general techniques used in thefront-end of the receiver such as signal detection and sensing the startof symbol are not explained here.

FIG. 3 shows a structure of the training signal according to thepreferred embodiment of the present invention.

As shown in FIG. 3, the training signal used in the OFDM wireless modemincludes continuous N_(s) short training signals (t₁˜t_(Ns)) of samplelength D, continuous two long training signals (T₁, T₂) of sample lengthN, and a guard interval (T_(GUARD)) interposed between the sets of shortand long training signals.

For example, the OFDM training structure of the IEEE 802.11a wirelessLAN consists of 10 short training symbols and two long training symbols.A guard interval interposes between the sets of the short and longtraining symbols.

FIG. 4 is a drawing illustrating effects of the frequency offsets and aninitial phase at the point of frequency offset compensation. The carrierfrequency synchronization method will be described with reference toFIG. 4 and through the mathematical signal analysis.

Firstly, the short training signal of the OFDM communication systemaccording to the preferred embodiment of the present invention isgenerated according to the equation 1.

$\begin{matrix}{{{S_{s}(n)} = {\sum\limits_{k = 0}^{N - 1}{{S_{s}(k)}{\mathbb{e}}^{\frac{{j2\pi}\; n}{N}}}}}{{n = 0},1,2,\ldots\;,{N - 1}}} & \text{〈Equation~~1〉}\end{matrix}$

where S_(s)(k) is the short training symbol and N is the size of theFFT/IFFT.

The short symbol s_(s)(n) of the period D repeats N/D times in timedomain such that the short training symbols are transmitted withrepetition of N_(s), times.

Since the signal may experience the phase jitter and Doppler shiftduring the propagation, the short training symbol can be expressed asthe following equation when the effect of the frequency offset isincluded.

$\begin{matrix}{{r_{s}(n)} = {{\sum\limits_{k = 0}^{N - 1}{{S_{s}(k)}{H(k)}{\mathbb{e}}^{\frac{{{j2\pi}{({k + ɛ})}}n}{N}}{\mathbb{e}}^{\frac{{j2\pi ɛ}{({n_{c} + {\Delta\; t}})}}{N}}}} + {W(n)}}} & \left\langle {{Equation}\mspace{14mu} 2} \right\rangle\end{matrix}$

where ε(=f_(offset)/Δf) is a normalized frequency offset and f_(offset)is a frequency offset, Δf is subcarrier spacing, and H(k) is channelresponse Δt is a signal reception start point (n=0), 2πΔt/N is initialphase rotation, N_(c) is a coarse mode start point, and W(n) is an addednoise.

As shown in equation 2, since the received signal r_(s)(n) of the periodD repeats N/D times, an approximate frequency offset can be estimatedusing the auto correlation characteristic in the coarse mode at stepS800.

In the coarse mode, the auto correlation characteristic of the shorttraining symbols t_(Ns−1)˜t_(Ns) is used for coarsely performing carrierfrequency synchronization.

The signal received at the RF module 100 is sent to the shift registerpart 311 via the A/D converter 200 and then the shift register part 311delays the training symbol in the received signal such that theconjugate complex numbers of the t_(Ns-i) and t_(Ns-i−1) are inputted tothe first multiplier 312-1 at the same time. The conjugate complexnumbers are multiplied in the conjugate complex number multiplier 312-1and then the output values from the conjugate complex number multiplier312-1 are accumulated in the accumulator 312-2 during the period of(i+1)*D. In the coarse mode, if two short training symbols are used, the“i” becomes 0 such that the accumulation is performed during the periodof D, and three short training symbols are used, the “i” becomes 2 suchthat the accumulation is performed during the period of 2D.

Next, the accumulated value is divided into the real and imaginary partsso as to calculate a ratio of the real part to the imaginary part suchthat an arc tangent table address is created using the ratio in thefirst divider 312-3. Consequently, the arctangent table address isstored in the argent table 312-4 in a predetermined sampling interval.

The phase converter 312-5 identifies the codes of the real and imaginaryparts of the accumulated value by referring to the divider 312-3 so asto transform the arctangent value outputted from the arctangent table312-4 into the corresponding region value and then outputs the carrierfrequency offset, {acute over (ε)}_(c,) which is calculated by equation3. Finally, the carrier frequency offset is estimated by multiplying theperiod N/D.

$\begin{matrix}\begin{matrix}{{\hat{ɛ}}_{c} = {\frac{N}{2\pi\; D}a\; r\;{g\left( {\sum\limits_{n = 0}^{L - 1}{{r_{s}\left( {n + D} \right)}{r_{s}(n)}^{*}}} \right)}}} \\{= {\frac{N}{2\pi\; D}a\; r\;{g\left( {\sum\limits_{n = 0}^{L - 1}{I\;{{m\left( \;{{r_{s}\left( {n + D} \right)}{r_{s}(n)}^{*}} \right)}/{\sum\limits_{n = 0}^{L - 1}{R\;{e\left( \;{{r_{s}\left( {n + D} \right)}{r_{s}(n)}^{*}} \right)}}}}}} \right)}}}\end{matrix} & \left\langle {{Equation}\mspace{14mu} 3} \right\rangle\end{matrix}$

where D is a distance between two symbols.

As shown in equation 3, the estimation range of the coarse frequencyoffset obtained using the auto correlation after delaying the trainingsignal sample using short training symbols is |{acute over(ε)}_(c)|<N/2D and the estimation accuracy depends on L(the number ofsamples). For example, in the IEEE 802.11a wireless LAN, the interval Dis 16 such that carrier estimation range of the coarse mode is |{acuteover (ε)}_(c)|<2. However, the estimation accuracy is low because thesample of L=N/4 taking an average is relatively small.

On the other hand, if the value L is greater than the interval D betweenthe two repeating symbols when estimating the frequency offset usingmore than 3 short training symbol in equation 3, the number of thesamples used for frequency offset estimation increases so as to reducethe noise such that the estimation range is maintained in |{acute over(ε)}_(c)|<N/2D and the estimation accuracy is improved.

In the case where the frequency offset is estimated using the number ofi short training symbols repeated in N/D times, the average can be takeni−1 times such that the frequency offset estimated by taking theaverages of i−1 times is more accurate than that of the frequency offsetobtained using just two short training signals.

For example, if the carrier frequency offset is estimated using 3 shorttraining symbols and L is 2D, the frequency offset can be obtained byaveraging the sum of the auto correlation value between the first andsecond short training symbols and the auto correlation value between thesecond and third short training symbols.

Since it is impossible to know how large the frequency offset isgenerated in the real environment, the frequency offset estimation mustbe performed in such a manner that the carrier frequency offset isroughly estimated in the coarse mode and then the frequency offset rangeof the long training symbol is narrowed using the estimated frequencyoffset of the coarse mode.

The long training symbol received through the channel is determined asequation 4.

$\begin{matrix}{{{r_{l}(n)} = {{\sum\limits_{k = 0}^{N - 1}{{S_{l}(k)}{H_{l}(k)}{\mathbb{e}}^{\frac{{{j2\pi}{({k + ɛ})}}n}{N}}{\mathbb{e}}^{\frac{{j2\pi ɛ}{({n_{f} + {\Delta\; t}})}}{N}}}} + {W_{l}(n)}}}{{n = 0},1,2,\ldots\mspace{11mu},{{2N} - 1}}} & \left\langle {{Equation}\mspace{14mu} 4} \right\rangle\end{matrix}$

where S₁ is a long training symbol, H₁(k) is a frequency response of thechannel, and n_(f) is a start point of the fine mode. In equation 4,r1(n) composed of N samples repeats twice.

The frequency offset value estimated at the frequency offset estimator310 is inputted into the first demultiplexer 330 such that thedemultiplexer 330 sends the demultiplexed signals to the bit expander321 according to the control signal S1 from the controller 10. In FIG. 1b, since the demultiplexed signals are processed with the same procedureafter the bit expending process, the signal {acute over (ε)} will beexemplary described without subscript for the notational convenience.

The signal from the demultiplexer 330 is shifted as much as log₂ N inthe rightward direction at the bit expander 321 in order to divide theestimated value from the estimation part 310 into the sample size N forthe FFT 400. Each sample is accumulated at the second accumulator 322such that the corresponding log function table address is assigned tothe sample.

The log function table address assigned at the accumulator 322 istransformed into an address in the corresponding range by referring tothe code values of the bit expander 321 in the first region controller323 such that the log function value stored in the address of the firstlog function table 324 is outputted.

The log function value from the first log function table 324 ismultiplied by the long training signal T₁(T₂) from the A/D converter 200in the second multiplier 325 so as to compensate frequency offset.

The signal compensated by the estimated frequency offset is sent to thefrequency offset compensator 310 and the second multiplier 325 by thesecond demultiplexer 350 according to the control signal S2 from thecontroller 10.

The long training symbol digitally compensated by the carrier frequencyoffset estimator in the coarse mode, at step 820, can be expressed asequation 5.

$\begin{matrix}\begin{matrix}\begin{matrix}{{y_{l}(n)} = {{r_{l}(n)}{\mathbb{e}}^{\frac{{- {j2\pi}}\;\hat{ɛ_{c}n}}{N}}}} \\{= {{\sum\limits_{k = 0}^{N - 1}{{S_{l}(k)}{H_{l}(k)}{\mathbb{e}}^{\frac{{{j2\pi}{({k + ɛ - {\hat{ɛ}}_{c}})}}n}{N}}{\mathbb{e}}^{\frac{{j2\pi ɛ}{({n_{f} + {\Delta\; t}})}}{N}}}} +}} \\{{w_{l}(n)}{\mathbb{e}}^{\frac{{- {j2\pi}}\;\hat{ɛ_{c}n}}{N}}}\end{matrix} \\{{n = 0},1,2,\ldots\mspace{11mu},{{2N} - 1}}\end{matrix} & \left\langle {{Equation}\mspace{14mu} 5} \right\rangle\end{matrix}$

In equation 5, the residual frequency offset {acute over (ε)}−{acuteover (ε)}_(c) exists, when the long training signal is compensated bythe frequency offset {acute over (ε)}_(c) estimated in the coarse mode.

Next, by using the compensated long training signal, the frequencyoffset is precisely estimated in the fine mode at step S820. Thefrequency offset estimation in the fine mode is performed in the samemanner as the frequency offset estimation in the coarse mode. In thiscase, the shift register part 311 delays the input signal as much assample size N, and the block used in the coarse mode for estimating thecoarse frequency offset is adopted in the following procedures.

The frequency offset can be estimated using equation 6 where the noiseis ignored, and the autocorrelation of the long training signalcompensated in the coarse mode is used.

$\begin{matrix}\begin{matrix}{{{\hat{ɛ}}_{f} \approx {ɛ - {\hat{ɛ}}_{c}}} = {\frac{1}{2\pi}a\; r\;{g\left( {\sum\limits_{n = 0}^{N - 1}{{y_{l}\left( {n + N} \right)}{y_{l}(n)}^{*}}} \right)}}} \\{= {\frac{1}{2\pi}a\; r\;{g\left( {\sum\limits_{n = 0}^{N - 1}{I\;{{m\left( {{y_{l}\left( {n + N} \right)}{y_{l}(n)}^{*}} \right)}/{\sum\limits_{n = 0}^{N - 1}{R\;{e\left( {{y_{l}\left( {n + N} \right)}{y_{l}(n)}^{*}} \right)}}}}}} \right)}}}\end{matrix} & \left\langle {{Equation}\mspace{14mu} 6} \right\rangle\end{matrix}$

In equation 6, the frequency offset {acute over (ε)}_(f) estimated inthe fine mode is more accurate than that estimated in the coarse modebecause more samples are used to obtain an average even though theestimation range is reduced to −0.5<{acute over (ε)}_(f)<0.5.

Accordingly, the long training signal from the second demultiplexer 350is compensated again using the frequency offset {acute over (ε)}_(f)estimated at the fine mode in the frequency offset compensation module320 at step S830.

The signal compensated by the frequency offset estimator in the finemode is expressed as equation 7.

$\begin{matrix}\begin{matrix}\begin{matrix}{{z_{l}(n)} = {{y_{l}(n)}{\mathbb{e}}^{\frac{{- {j2\pi}}\;\hat{ɛ_{j}n}}{N}}}} \\{= {{\sum\limits_{k = 0}^{N - 1}{{S_{l}(k)}{H_{l}(k)}{\mathbb{e}}^{\frac{{{j2\pi}{({k + ɛ - \hat{ɛ}})}}n}{N}}{\mathbb{e}}^{\frac{{j2\pi}\;{ɛ{({n_{f} + {\Delta\; t}})}}}{N}}}} +}} \\{{w_{l}(n)}{\mathbb{e}}^{\frac{{- {j2\pi}}\;\hat{ɛ}\; n}{N}}}\end{matrix} \\{{n = 0},1,2,\ldots\mspace{11mu},{{2N} - 1}}\end{matrix} & \left\langle {{Equation}\mspace{14mu} 7} \right\rangle\end{matrix}$

As described above, in the frequency synchronization method of thepresent invention, the signal can be digitally compensated using thefrequency offset estimator with a broad estimation range and highprecision using the coarse and fine modes. The coarse and fine modesshare the same hardware for frequency offset estimation operation.

The long training signal compensated according to equation 7 istransformed in the FFT 400, and the channel estimator 450 estimates thecoefficients of the equalizer 500 using the zero-forcing method at stepS840.

To simplify the mathematical expression, it is assumed that the effectsof noise and residual frequency offset ε−{acute over (ε)}_(c) areignorable. In this case, the amplitude distortion is reduced because theresidual frequency offset is very small so that only the phasedistortion remains.

Accordingly, the effects of the residual frequency offset remaining inthe long training signal after the initial synchronization can beapproximated to the following form distorted just in phase as theequation 8 if the effect from the noise is ignored.

$\begin{matrix}\begin{matrix}\begin{matrix}{{Z_{l}(k)} = {{FFT}\left( {z_{l}(n)} \right)}} \\{= {{\frac{1}{N}{\sum\limits_{k = 0}^{N - 1}{\left( {\sum\limits_{k = 0}^{N - 1}{{S_{l}(k)}{H_{l}(k)}{\mathbb{e}}^{\frac{{{j2\pi}{({k + ɛ - \hat{ɛ}})}}n}{N}}}} \right){\mathbb{e}}^{\frac{{- {j2\pi}}\; n\; k}{N}}{\mathbb{e}}^{\frac{{j2\pi}\;{ɛ{({n_{f} + {\Delta\; t}})}}}{N}}}}} + {W_{l}^{\prime}(k)}}}\end{matrix} \\{{{\hat{H}}_{l}(k)} = {\frac{Z_{l}(k)}{S_{l}(k)} \cong {{H_{l}(k)}{\mathbb{e}}^{\frac{{{j\pi}{({ɛ - \hat{ɛ}})}}{({N - 1})}}{N}}{\mathbb{e}}^{\frac{{j2\pi}{({n_{f} + {\Delta\; t}})}}{N}}}}}\end{matrix} & \left\langle {{Equation}\mspace{14mu} 8} \right\rangle\end{matrix}$

In the equation 8, the channel estimate Ĥ_(I)(k) includes the initialphase rotation amont 2πεΔt, and a fine mode initial rotation amount2πεn_(f)/N. The complete digital compensation of the signal can beachieved since the data symbol is compensated together with the initialphase rotation amount included in the channel estimates, even though itis difficult to estimate the initial phase rotation amount because it isunable to calculate a start point thereof.

The next data symbol inputted to the second multiplier 325 from the A/Dconverter 200 is compensated using the log function value correspondingto the frequency offset {acute over (ε)}≈{acute over (ε)}_(f)+{acuteover (ε)}_(c) resulting from multiplying the frequency offset estimatedin the fine and coarse modes in the adder 340 such that the carrierfrequency synchronization is achieved at step S850. In this case theadder 340 adds the frequency offsets estimated in the coarse and finemodes and sends the result to the bit expander according to the controlsignal S1 from the controller 10. The following processes are same inboth coarse and fine mode.

When the data symbol is compensated using the log function valuecorresponding to the address {acute over (ε)}≈{acute over(ε)}_(f)+{acute over (ε)}_(c), an ith OFDM symbol is expressed asequation 9.

$\begin{matrix}{\begin{matrix}{{y_{i}\left( \overset{\sim}{n} \right)} = {{\sum\limits_{k = 0}^{N - 1}{{X_{i}(k)}{H_{i}(k)}{\mathbb{e}}^{\frac{{{j2\pi}{({k + ɛ - \hat{ɛ}})}}\overset{\sim}{n}}{N}}{\mathbb{e}}^{\frac{{j2\pi}\;{ɛ{({n_{d} + {\Delta\; t}})}}}{N}}}} +}} \\{{w_{i}\left( \overset{\sim}{n} \right)}{\mathbb{e}}^{\frac{{- {j2\pi}}\;\hat{ɛ}\;\overset{\sim}{n}}{N}}}\end{matrix}{{n = 0},1,\ldots\mspace{11mu},{N + N_{G} - 1}}} & \left\langle {{Equation}\mspace{14mu} 9} \right\rangle\end{matrix}$

where X_(i)(k) is the data transmitted on the ith subcarrier, Hi(k) isthe channel response, n_(d) is an index where the data symbolcompensation starts in time domain, and N_(G) is the size of guardinterval.

As indicated in the equation 9 and FIG. 4, the positions of channelestimation using the long training signal and the data compensationusing the estimated carrier frequency offset are not identical.Therefore, after data symbols compensated by the frequency offsetestimator are transformed using FFT 400 at step S860 and thencompensated using the estimated channel in the equalizer 500 at stepS870, the same phase rotation occurs to all the data symbols. The phaserotation can be compensated by the Frequency Domain Equalizer (FEQ) 500.

FIG. 4 is a drawing illustrating the effects of the frequency offsetsand an initial phase at the frequency offset compensation point, andFIG. 5 is a drawing illustrating the effects of carrier frequencyoffsets of the data symbols.

As shown in FIG. 4, even though the data symbol is compensated throughthe two step compensation method, the residual frequency offset existssuch that the phase rotation by the residual frequency offset givescritical effect to the data symbol if the received symbols is over apredetermined number.

In this case, since the residual frequency offset remained in the i_(th)OFDM symbol received during the initial synchronization process is verysmall, the signal transformed in the FFT after deleting the guardinterval from the i_(th) OFDM symbol can be expressed as equation 10,where the noise is ignored for simplifying the equation.

$\begin{matrix}\begin{matrix}{{Y_{i}(k)} = {{FFT}\left( {y_{i}(n)} \right)}} \\{= {{\frac{1}{N}{\sum\limits_{k = 0}^{N - 1}{\left( {\sum\limits_{k = 0}^{N - 1}{{X_{i}(k)}{H_{i}(k)}{\mathbb{e}}^{\frac{{{j2\pi}{({k + ɛ - \hat{ɛ}})}}n}{N}}}} \right){\mathbb{e}}^{\frac{{- {j2\pi}}\; n\; k}{N}}{\mathbb{e}}^{\frac{{j2\pi}\;{ɛ{({n_{d} + {\Delta\; t}})}}}{\;}}}}} + {W_{i}^{\prime}(k)}}} \\{\cong {{X_{i}(k)}{H_{i}(k)}{\mathbb{e}}^{\frac{{{{j2\pi}{({ɛ - \hat{ɛ}})}}{\{{{N{({i - 1})}} + {i\; N_{G}}}\}}} + {{{j\pi}{({ɛ - \hat{ɛ}})}}{({N - 1})}}}{N}}{\mathbb{e}}^{\frac{{j2\pi}\;{ɛ{({n_{d} + {\Delta\; t}})}}}{N}}}}\end{matrix} & \left\langle {{Equation}\mspace{14mu} 10} \right\rangle\end{matrix}$

where e^(jπε(n) ^(d) ^()+Δt/N) is the initial phase where the datasymbol begins, and e^(j2π(ε−{circumflex over (ε)}) ^(t) ^(){N(t−1)+iN)^(G) ^(}/N) is the initial phase rotation caused by deleting the guardinterval of the i_(th) data symbol.

The channel distortion is compensated using the channel value estimatedby equation 8. Supposed that the channel experienced by the longtraining signal and the channel of the data sequence are identical,i.e., H₁(k)=H_(i)(k), the equation can be simplified as equation 11.

$\begin{matrix}\begin{matrix}{{\hat{X}(k)} = \frac{Y_{i}(k)}{\hat{H}(k)}} \\{\cong \frac{{X_{i}(k)}{H_{i}(k)}{\mathbb{e}}^{\frac{{{{j2\pi}{({ɛ - \hat{ɛ}})}}{\{{{N{({i - 1})}} + {iN}_{G}}\}}} + {{{j\pi}{({ɛ - \hat{ɛ}})}}{({N - 1})}}}{N}}{\mathbb{e}}^{\frac{{j2\pi}\;{ɛ{({n_{d} + {\Delta\; t}})}}}{N}}}{{H_{l}(k)}{\mathbb{e}}^{\frac{{{j\pi}{({ɛ - \hat{ɛ}})}}{({N - 1})}}{N}}{\mathbb{e}}^{\frac{{j2\pi}\;{ɛ{({n_{d} + {\Delta\; t}})}}}{N}}}} \\{\cong {{X_{i}(k)}{\mathbb{e}}^{\frac{{{j2\pi}{({ɛ - {\hat{ɛ}}_{i}})}}{\{{{N{({i - 1})}} + {iN}_{G}}\}}}{N}}{\mathbb{e}}^{\frac{{j2\pi}\;{ɛ{({n_{d} - n_{f}})}}}{N}}}}\end{matrix} & \left\langle {{Equation}\mspace{11mu} 11} \right\rangle\end{matrix}$

If the residual frequency offset is 0 in equation 11, it can be muchsimplified as following equation.

$\begin{matrix}{{{\hat{X}}_{i}(k)} = {{X_{i}(k)}{\mathbb{e}}^{\frac{{j2\pi}\;{ɛ{({n_{d} - n_{f}})}}}{N}}}} & \left\langle {{Equation}\mspace{11mu} 12} \right\rangle\end{matrix}$

As shown in equation 11 and equation 12, the channel estimation positionn_(f) is not identical to the data symbol compensation position n_(d),leading to the phase rotation as much as j2πε(n_(d)−n_(f))/N. Note thatthe phase rotation caused by the residual frequency offset increases inproportional to the symbol index i.

On the other hand, if the data symbol is compensated in such a mannerthat the channel is estimated using the long training signal of whichthe carrier frequency offset is compensated in the condition of n=n_(f)when n=0, and the index is increased from n=n_(d), then the phaserotation problem in equation 11 can be solved.

However, since the phase to be compensated is j2π{circumflex over(ε)}n_(f) if the index is increased from n=n_(f) and when n is 0,additional hardware is required because the accumulator adds n_(f) orthe multiplier should be used to obtain the phase.

In the present invention, the index increases from 0 while thecompensations of the long training signal and the data symbol in thetime domain such that the phase to be compensated for each sample can beobtained only using the accumulator and there is no need to calculatepresently how many sample periods are far from the point of signalreception.

The phase rotation at equation 12 is estimated in such a manner ofestimating the phase rotation caused by the residual frequency offset inthe residual estimation part 600 together with the phase rotation amountfor compensating the effect of the residual frequency offset afterpassing the equalizer 500. Accordingly, there is no need of theadditional hardware for compensating the phase rotation because the datasymbol is compensated by increasing the index from 0 in time domain.

The residual estimation part 600 extracts pilot signal of each symbol inthe tracking mode and compensates, in frequency domain, the phaserotation caused by the residual frequency offset existing even after thecompensation of carrier frequency using the autocorrelation.

A pilot extractor 610 of the residual phase estimation part 600 extractsthe pilot signal and sends the pilot signal to the first multiplier312-1 of the selective estimation part 312 such that the selectiveestimation part 312 estimates the phase rotation caused by thedifference between the point of the residual frequency and channelestimation and the point of the data symbol compensation in time domainat step S880. The residual phase offset can be calculated using theautocorrelation of the pilot signal in the tracking mode as equation 13.

$\begin{matrix}\begin{matrix}{\hat{\phi} = {\tan^{- 1}\left( {\sum\limits_{p = 0}^{P - 1}\;{{{\hat{X}}_{i}(p)}{X_{i}(p)}^{*}}} \right)}} \\{= \frac{2{\pi\left\lbrack {{\left( {ɛ - \hat{ɛ}} \right)\left\{ {{N\left( {i - 1} \right)} + {iN}_{G}} \right\}} + {ɛ\left( {n_{d} - n_{f}} \right)}} \right\rbrack}}{N}}\end{matrix} & \left\langle {{Equation}\mspace{11mu} 13} \right\rangle\end{matrix}$

where

${\overset{p}{X}}_{i}(p)$is the p_(th) pilot signal in the received signal

${{\overset{p}{X}}_{i}(k)},$and X_(i)(p) is the p_(th) pilot signal of the i_(th) OFDM symbol.

As shown in equation 13, when estimating the phase rotation by theresidual frequency using the autocorrelation of the pilot signal in thetracking mode, the phase rotation caused by difference between thechannel estimation point and the data symbol compensation point is alsoestimated.

A second region controller 621 of the residual compensation part 620generates a second log function table address corresponding to theresidual phase value from the first demultiplexer 330 of the selectiveestimator 312.

The second log function table 622 outputs one of the log function valueswhich is sampled in a predetermined interval and stored thereinaccording to the second log function address from the second regioncontroller 621 and the third multiplier 623 compensates the log functionvalue from the second log function table 622 by multiplying the logfunction value with the compensated data symbol at step S890.

The data symbol compensated in the residual phase compensation part 620using the phase rotation value estimated to every symbols in the pilotextractor 610 and the estimation part 310 is expressed as equation 14.

$\begin{matrix}\begin{matrix}{{{\overset{\sim}{X}}_{i}(k)} = {{{\hat{X}}_{i}(k)}{\mathbb{e}}^{\frac{{- j}{\hat{\phi}}_{i}}{N}}}} \\{\cong {X_{i}(k)}}\end{matrix} & \left\langle {{Equation}\mspace{11mu} 14} \right\rangle\end{matrix}$

In equation 14, the signal passed through the residual phasecompensation part 620 shows that the phase rotation caused by thedifference between the residual frequency offset/channel estimationpoint and the data symbol compensation point is compensated.

The residual phase compensated-signal loops from the step S850 to thestep S895 until it is to be the last data symbol, and then is sent to aviterbi decoder via a demodulator 700.

Even though the selective estimation part 312 is shared for reducing thehardware needed for residual phase tracking in the preferred embodimentof the present invention, another circuit identical to the selectiveestimation part 312 can be implemented.

Also, in the OFDM wireless burst modem using one of the trainingsignals, its frequency synchronization method is similar to the 2 stepmethod and the same hardware can be used.

FIG. 6 is a drawing illustrating effects of the carrier frequencyoffsets and an initial phase at an offset compensation point in a singlestep frequency offset synchronization method using one type trainingsignal. In this case the procedure for synchronizing the carrierfrequency offset using one type training signal is same with thefrequency synchronization method of FIG. 2 b without the coarse mode,i.e., {circumflex over (ε)}=0.

FIG. 1 d is a block diagram illustrating the operation of the frequencysynchronization part of FIG. 1 b when using single training signal. InFIG. 1 d the adder 340 and the second demultiplexer 350 are not depictedfor simplifying the drawing.

Referring to FIG. 1 d and FIG. 6, the training signal consists of T_(t1)and T_(t2) each having D_(t) samples. In this case the training signalcan be expressed as equation 15.

$\begin{matrix}{{{r_{i}(n)} = {{\sum\limits_{k = 0}^{N - 1}\;{{S_{t}(k)}{H_{i}(k)}{\mathbb{e}}^{\frac{{{j2\pi}{({k + ɛ})}}n}{N}}{\mathbb{e}}^{\frac{{j2\pi}\;{\Delta t}}{N}}}} + {w_{t}(n)}}}{{n = 0},1,2,\ldots\mspace{11mu},{{2\; D_{t}} - 1}}} & \left\langle {{Equation}\mspace{11mu} 15} \right\rangle\end{matrix}$

where S_(t)(k) is the training signal in the frequency domain andH_(t)(k) is the frequency response of the long training signal. Δt isthe beginning point (n=0) of the signal reception and 2πΔt/N is theinitial phase rotation.

Since the same signals are repeatedly received in D_(t) samples, thecarrier frequency offset is estimated using the autocorrelation of thereceived signals at step S900. The frequency offset can be expressed asequation 16.

$\begin{matrix}\begin{matrix}{{\hat{ɛ}}_{t} = {\frac{N}{2\pi\; D_{t}}{\arg\left( {\sum\limits_{n = 0}^{D_{t} - 1}\;{{r_{t}\left( {n + D_{t}} \right)}{r_{t}(n)}^{*}}} \right)}}} \\\left. {= {\frac{N}{2\pi\; D_{t}}{{\arg\left( {\sum\limits_{n = 0}^{D_{t} - 1}\;{{{Im}\left( {r_{t} + D_{t}} \right)}{r_{t}(n)}^{*}}} \right)}/{\sum\limits_{n = 0}^{D_{t} - 1}\;{{Re}\left( {{r_{t}\left( {n + D_{t}} \right)}{r_{t}(n)}^{*}} \right)}}}}} \right)\end{matrix} & \left\langle {{Equation}\mspace{11mu} 16} \right\rangle\end{matrix}$

In equation 16, the carrier frequency offset estimation range is

ɛ̂_(t) < N/2D_(t)when using one type training signal. In the case of D_(t)=D<N, theestimation range is

ɛ̂_(t) < N/2Dwhich is the same as the estimation result obtained by using the shorttraining signal in the 2 step frequency offset synchronization as inequation 3.

The signal compensated in the training signal and the data symbol usingthe estimated frequency offset {circumflex over (ε)}_(t) can beexpressed as equation 17.

$\begin{matrix}\begin{matrix}\begin{matrix}{{y_{i}(n)} = {{r_{i}(n)}{\mathbb{e}}^{\frac{{- {j2\pi}}\;{\hat{ɛ}}_{i}n}{N}}}} \\{= {{\sum\limits_{k = 0}^{N - 1}\;{{S_{i}(k)}{H_{t}(k)}{\mathbb{e}}^{\frac{{{j2\pi}{({k + ɛ - \hat{ɛ}})}}n}{N}}{\mathbb{e}}^{\frac{{j2\pi}\;{ɛ\Delta}\; t}{N}}}} + {{w_{i}(n)}{\mathbb{e}}^{\frac{{- {j2}}{\hat{ɛ}}_{i}n}{N}}}}}\end{matrix} \\{{n = 0},1,2,\ldots\mspace{11mu},{D_{t} - 1}}\end{matrix} & \left\langle {{Equation}\mspace{11mu} 17} \right\rangle\end{matrix}$

In equation 17, the channel can be estimated using the training signalwhen the training signal has only the long training signals, i.e., Dt=N.The channel estimation is performed on the basis of the FFT and zeroforcing at step S920. In this case, since the effects of noise isignored and the training signal is compensated using the estimatedcarrier frequency offset, the effect of the residual frequency offsetremained in the training signal during the channel estimation can beapproximated as in equation 18 where only the phase is distorted.

$\begin{matrix}\begin{matrix}\begin{matrix}{{{\hat{H}}_{i}(k)} = \frac{{FFT}\left( {y_{i}(n)} \right)}{S_{i}(k)}} \\{\cong {{H_{i}(k)}{\mathbb{e}}^{\frac{{{j\pi}{({ɛ - \hat{ɛ}})}}{({N - 1})}}{N}}{\mathbb{e}}^{\frac{{j2\pi}\; ɛ\;\Delta\; t}{N}}}}\end{matrix} \\{{k = 0},1,\ldots\mspace{11mu},{N - 1}}\end{matrix} & \left\langle {{Equation}\mspace{11mu} 18} \right\rangle\end{matrix}$

where

${\mathbb{e}}^{\frac{{{j2\pi}{({ɛ - \hat{ɛ}})}}{({N - 1})}}{N}}$is the phase rotation caused by the residual frequency offset. Since thechannel estimation value Ĥ_(t)(k) includes the initial phase rotationamount

$\frac{2\pi\;{ɛ\Delta}\; t}{N}$like in equation 8, an unknown initial phase rotation can be compensatedif the data symbol is compensated using the channel estimation value,resulting in complete digital compensation.

In the synchronization method using only one type training signal, thechannel estimation point and the compensation point is same such thatthe phase rotation caused by the difference between the channelestimation and channel compensation points does not exist.

The i_(th) received OFDM data symbol including the guard interval can beexpressed as equation 19 after compensation of carrier frequency offset{circumflex over (ε)}_(t).

$\begin{matrix}\begin{matrix}{\begin{matrix}{{y_{i}\left( \overset{\sim}{n} \right)} = {r_{i}(n)}^{\frac{{- {j2\pi}}\;{\hat{ɛ}}_{i}\overset{\sim}{n}}{N}}} \\{= {{\sum\limits_{k = 0}^{N - 1}\;{{X_{i}(k)}{H_{i}(k)}{\mathbb{e}}^{\frac{{{j2\pi}{({k + ɛ - {\hat{ɛ}}_{t}})}}\overset{\sim}{n}}{N}}{\mathbb{e}}^{\frac{{j2\pi}{\{{{ɛ\;\Delta\; t} + {{({ɛ - {\hat{ɛ}}_{t}})}n_{t}}}\}}}{N}}}} +}} \\{{w_{i}(n)}^{\frac{{- {j2\pi}}\;{\hat{ɛ}}_{t}\overset{\sim}{n}}{N}}}\end{matrix}{{\overset{\sim}{n} = 0},1,\mspace{14mu}\ldots\mspace{14mu},{N + N_{G} - 1}}} & \;\end{matrix} & \left( {{Equation}\mspace{14mu} 19} \right)\end{matrix}$

where X_(i)(k) is a signal in the frequency range of the i_(th) data,H_(i)(k) is the frequency response of the i_(th) data symbol, and n_(t)is the carrier frequency offset estimation-beginning point.

The frequency offset compensated-data symbol is transformed in the FFTat step S940, and the i_(th) OFDM data symbol is equalized using theestimated channel value in the equalizer 500 at step S950. In this case,supposed that the effect of the noise is ignored and the channel doesnot change, i.e., H_(I)(k)=H_(i)(k), the equation can be simplified asequation 20.

$\begin{matrix}\begin{matrix}{{{\hat{X}}_{i}(k)} = \frac{{FFT}\left( {y_{i}(n)} \right)}{{\hat{H}}_{t}(k)}} \\{\cong \frac{{X_{i}(k)}{H_{i}(k)}{\mathbb{e}}^{\frac{{{{j2\pi}{({ɛ - {\hat{ɛ}}_{i}})}}{\{{{N{({i - 1})}} + {iN}_{G} + n_{i}}\}}} + {{{j\pi}{({ɛ - \hat{ɛ}})}}{({N - 1})}}}{N}}{\mathbb{e}}^{\frac{{j2\pi}\; ɛ\;\Delta\; t}{N}}}{{H_{t}(k)}{\mathbb{e}}^{\frac{{{j\pi}{({ɛ - \hat{ɛ}})}}{({N - 1})}}{N}}{\mathbb{e}}^{\frac{{j2\pi}\; ɛ\;\Delta\; t}{N}}}} \\{{X_{i}(k)}{\mathbb{e}}^{\frac{{{j2\pi}{({ɛ - {\hat{ɛ}}_{i}})}}{\{{{N{({i - 1})}} + {iN}_{G} + n_{i}}\}}}{N}}}\end{matrix} & \left( {{Equation}\mspace{14mu} 20} \right)\end{matrix}$where

${\mathbb{e}}^{\frac{{{j2\pi}{({ɛ - {\hat{ɛ}}_{i}})}}{\{{{N{({i - 1})}} + {iN}_{G} + n_{i}}\}}}{N}}$is the initial phase generated by deleting the guard interval of thei_(th) OFDM symbol. In equation 20, the residual frequency is very smallsince the data symbol is the result compensated by the estimated carrierfrequency offset.

In comparison between equation 11 and equation 20, there is no phaserotation

$e^{\frac{{j2}\;\pi\;{ɛ{({n_{d} - n_{f}})}}}{N}}$in one step method as expressed by equation 11 because the channelestimation and compensation is performed at the same position. On theother hand, the phase rotation caused by the residual frequency offsetincreases in proportional to the symbol index i in the two step methodas expressed by equation 20 such that the effect of the residualfrequency offset causes critical problem after the number ofpredetermined symbols.

Accordingly, the phase tracking process for compensating the phaserotation caused by the residual frequency is performed using pilotsignal included in each data symbol. The phase rotation caused by theresidual frequency is estimated using the autocorrelation of the pilotsignals at step S960. The phase rotation can be expressed as equation21.

$\begin{matrix}\begin{matrix}{\hat{\phi_{i}} = {\tan^{- 1}\left( {\sum\limits_{P = 0}^{P - 1}\;{{{\hat{X}}_{i}(p)}{X_{i}(p)}^{*}}} \right)}} \\{= \frac{2{\pi\left( {ɛ - ɛ_{i}} \right)}\left\{ {{N\left( {i - 1} \right)}^{\bigwedge} + {iN}_{G} + n_{t}} \right\}}{N}}\end{matrix} & \left( {{Equation}\mspace{14mu} 21} \right)\end{matrix}$where {circumflex over (X)}_(t)(p) is the p_(th) pilot signal in thereceived signal {circumflex over (X)}_(t)(k) and X_(t)(p) is the p_(th)pilot symbol of the i_(th) transmitted OFDM symbol.

The estimated phase rotation is compensated at step S970 and thecompensated signal can be expressed as equation 22.

$\begin{matrix}\begin{matrix}{{{\overset{\sim}{X}}_{i}(k)} = {{{\hat{X}}_{i}(k)}{\mathbb{e}}^{\frac{{- j}{\hat{\phi}}_{i}}{N}}}} \\{\cong {X_{i}(k)}}\end{matrix} & \left( {{Equation}\mspace{14mu} 22} \right)\end{matrix}$

As shown in equation 22, it is possible to digitally synchronize carrierfrequency in the one step method using only the long training signal ofD_(t)=N through the same processes as in the two step method.

In case only the short training signal of D_(t)=D is used, a measure forestimating the channel is considered even though the processes forestimating and compensating the frequency offset are same with themethod using only the long training signal. Generally, since the Dsamples become non-zero value and N−D samples become zeros if therepeated signals are transformed by the FFT, it is impossible tocalculate the channel just using the short training signal relative toall the sub-channels on the basis of the zero forcing. In this case,channel estimation should be performed using special method such as aninterpolation or another training signal should be adapted forestimating the channel.

As explained above, in the apparatus and method for synchronizingfrequency in the OFDM communication system, the same hardware andprocesses can be used in the two step method using long training andshort training signals and the one step method just using short trainingsignal or even when using short training signal in case of additionaltraining signal being for channel estimation.

How the arctangent function table and the first and second log functiontables of the present invention are implemented will be describedhereinafter.

The hardware complexity and the computation accuracy of the apparatusand method for OFDM frequency synchronization of the present inventiondepends on the arctangent table 312-4 and the log function tables.Accordingly, it is need to reduce the size of the tables and enhance thecomputation accuracy.

FIG. 7 shows graphs for illustrating the implementation of an arctangenttable according to the present invention.

Generally, the tangent curve repeats 4 times in its shape in the rangeof [−π˜π] with different signs. Accordingly, in the present inventionthe tangent curve in the range of [0˜π/2] is stored in the table and thearctangent value outputted from the phase converter 312-5 according tothe signs of the real and imaginary parts of the divider 312-3.

In this case an arctangent input range corresponding to the output range[0˜π/2] is [0˜8]. However, since over 90% of the arctangent outputs areconcentrated in the input range of [0˜8], the arctangent input islimited to the range of [0˜8] (see FIG. 7 a) and it is preferred to takegraded samples according to the gradient of the arctangent.

In equations 3 and 6,

$\frac{1}{2\pi}$is multiplied to the carrier frequency offset. To remove this, the datais stored after multiplied by

$\frac{1}{2\pi}$when arctangent table is implemented. Accordingly, the arctangent outputrange becomes [1˜1/4].

FIG. 8 is a drawing for illustrating a phase adjustment method of thepresent invention.

As explained above, since the values in the range of [0˜π/2] are storedin the arctangent table, the phase converter 312-5 outputs arctangentvalues using the signs of the real and imaginary parts of theaccumulated data from the divider 312-3.

The reason why the phase adjustment standard is not 1/2π but just 1/2 isbecause the output range of the arc tangent table 312-4 is [0˜1/4].

While, a difference between the equation 3 and 6 is the part of N/D ofequation 3, i.e., N/D is multiplied to the arctangent output whenestimating the frequency offset in the coarse mode such that in thecoarse mode the arctangent output is shifted as much as 2 bits inleftward direction. In this case an arithematical bit expansion shouldbe executed in addition to the 2-bit shift for preventing the accuracyof the arctangent from being fallen.

The arctangent table implemented as above has a small hardwarecomplexity and can be used in the coarse and fine modes in the samemanner. Furthermore, since the outputs of the divider 312-3 correspondto the arctangent table addresses, there is no need of additionalhardware for creating addresses.

On the other hand, the output of the frequency offset compensationmodule can be expressed as equation 23.

$\begin{matrix}\begin{matrix}{{c(n)} = {\mathbb{e}}^{\frac{{- {j2\pi}}\; ɛ\;\hat{ɛ}\; n}{N}}} \\{= {{\cos\left( \frac{2\pi\;\hat{ɛ}\; n}{N} \right)} - {j\;{\sin\left( \frac{2\pi\;\hat{ɛ}\; n}{N} \right)}}}}\end{matrix} & \left( {{Equation}\mspace{14mu} 23} \right)\end{matrix}$

where {circumflex over (ε)} is an estimated frequency offset and has avalue of {circumflex over (ε)}={circumflex over (ε)}_(c), {circumflexover (ε)}={circumflex over (ε)}_(f), {circumflex over (ε)}={circumflexover (ε)}_(f)+{circumflex over (ε)}_(c), and {circumflex over(ε)}={circumflex over (ε)}_(t) according to the tracking mode. As shownin equation 23, the log function table consists of sine and cosine tableso as to create output at every clock tick.

FIG. 9 is a pair of drawings showing the sine and cosine waveforms. Asshown in FIG. 9, each of the sine and cosine curves has a wavelengthwhich is divided into 4 regions numbered from 0 to 3. Once the logfunction table is created using function values in the range of [0˜π/2],i.e., region 0, the function values in other regions 1, 2 and 3 can beobtained using the function values of region 0.

Also, in order to simply create the log function table, it is preferredto normalize the input values of the log function table to 2π such thatthe actual input range is to be [0˜1/4].

As such, 2π of the equation 14 can be ignored such that the

$\frac{\hat{ɛ}\; n}{N}$corresponds to the addresses in the sine and cosine tables and if

$\frac{\hat{ɛ}\; n}{N}$becomes greater than 1/4 the region is shifted.

The estimated frequency offset {circumflex over (ε)} is accumulated inthe second accumulator 322 at every clock ticks such that the secondaccumulator 322 creates addresses of the log function table. In thiscase the bit expander 321 previously divides estimation value by N suchthat the number of bits of the second accumulator 322 can be fixed.

FIG. 10 is a drawing for illustrating the operation of a bit expander ofthe frequency synchronization apparatus of the present invention.

Let's suppose that the estimated frequency offset is expressed in 13bits, 3 bits are located left side of a floating point, and the mostleft bit is a sign bit.

The estimated frequency offset is shifted 6 positions to the left so asto be divided by N(=64).

Next, the left bits from the point of 1/4 is removed and 15 bits of

$\frac{\hat{ɛ}}{N}$is outputted. The output of the second accumulator can be expressed asequation 24.

$\begin{matrix}{\frac{\hat{ɛ}\; n}{N} = {\frac{\hat{ɛ}\;\left( {n - 1} \right)}{N} + \frac{\hat{ɛ}}{N}}} & \left\langle {{Equation}\mspace{11mu} 24} \right\rangle\end{matrix}$

As described above, since the input range of the sine and cosine tableis [0˜1/4], accurate sine and cosine function values cannot be obtainedif the output from the second accumulator 322 is out of the range.However, the output value from the second accumulator 322 increases dueto the every clock accumulation and this problem is solved by the firstregion controller 323.

Since the estimated frequency offset is inputted to the secondaccumulator 322 after being divided by N, the output from the secondaccumulator cannot be a value in other ranges. That is, if the result ofaccumulation to the n−1,

$\frac{\hat{ɛ}\;\left( {n - 1} \right)}{N},$is in the region 0, the accumulation result to n,

$\frac{\hat{ɛ}\; n}{N},$can exist in the region 0 or region 1, but not in the region 3 or region2. The region shift depends on whether the accumulation result isgreater than 1/4 or not. This can be expressed as equation 25.

$\begin{matrix}{{{{{if}\mspace{14mu}\frac{\hat{ɛ}\; n}{N}} \geq \frac{1}{4}}\frac{\hat{ɛ}\; n}{N} = {\frac{\hat{ɛ}\; n}{N} - \frac{1}{4}}}{{region} = {{region} + 1}}{else}{\frac{\hat{ɛ}\; n}{N} = \frac{\hat{ɛ}\; n}{N}}{{end},{{where}\mspace{14mu}{``{region}"}\mspace{14mu}{is}\mspace{14mu} a\mspace{14mu}{present}\mspace{14mu}{{region}.}}}} & \left\langle {{Equation}\mspace{11mu} 25} \right\rangle\end{matrix}$

The first region controller 323 identifies the output from the secondaccumulator 322 and bypasses the output if the output is less than 1/4.On the other hand, if the output is greater than 1/4, the first regioncontroller 323 generates an output by subtracting 1/4 from the outputand shifts the present region to next region.

In FIG. 10, if the fourteenth position bit is 1 on actually implementinghardware, the output of the second accumulator 322 is greater than 1/4such that the first region controller 323 can be simply implemented byresetting the fourteenth bit position to 0 and shifting the region.

Also, the function values in the region 2 where only the sign isopposite to that of the region 0 is simply obtained using the functionvalues of the region 0. Even though the function values of the region 1and region 3 that are symmetrically positioned to the region 0 areimpossible to be directly obtained using the table, the cosine and sinevalues can be obtained from respective sine and cosine tables withoutchanging the tables.

This will be explained with an example of a table having a size 4 withreference to FIG. 11. FIG. 11 is a drawing for illustrating addresscreation in a sine and cosine tables in accordance with region.

In FIG. 11, if the output of the second accumulator 322 is in the region0 and the value of the output is 11, the next output of the secondaccumulator 322 becomes 100 such that the first region controller 323performs region control. However, the output value of the address 11 isnot obtained since the value of the address 00 is 0.

While, as explained in FIG. 7 the data of address 00 in the region 1 isidentical to the data of address 11 in the log function table, the dataof address 10 in the region 1 is identical to the data of address 01 inthe log function table. That is, the output of the second accumulator322 must be complemented before being stored as an address in the logfunction table. In this manner, the function values of all the regionscan be obtained using the lookup table implemented with the region 0.

By implementing the frequency offset compensation module according tothe above explained method, the hardware size can be reduced.

FIG. 1 e is a block diagram for illustrating the residual phase trackingpart wherein the imaginary part of the pilot signal is 0 and the realpart of the pilot signal is 0, 1, or −1.

In FIG. 1 e, the residual phase compensation part 620 has a similarstructure with the frequency synchronization module 300. Since theestimation module 310 is used in initial synchronization, the estimationmodule is shared by the residual phase estimation part as explainedabove.

In case that the imaginary part of the pilot signal is 0 and the realpart of the pilot signal is 0, 1, or −1 as in the IEEE 802.11a wirelessLAN, the first conjugate complex number multiplier 312-1 can be replacedby a sign changing part 313. That is, the sign changing part 313 outputs0 if the real part of the pilot signal is 0, outputs the input data asit is if the real part is 1, and outputs the input data after changingits sign into opposite sign if the real part is −1.

On the other hand, the residual phase compensation part 620 differs fromthe frequency offset compensation module 320 except for the sine andcosine tables. Furthermore, since the frequency offset compensationmodule 320 must constantly compensate the input data symbol, it can beshared by the residual phase compensation part 620. Accordingly, theresidual phase compensation part 620 can be simply implemented relativeto the frequency offset compensation module 320 because the phaseinputted to the sine and cosine tables are not changed in one symboltime even though the residual phase compensation part 620 has the sineand cosine tables.

While this invention has been described in connection with what ispresently considered to be the most practical and preferred embodiment,it is to be understood that the invention is not limited to thedisclosed embodiments, but, on the equivalent arrangements includedwithin the spirit and scope of the appended claims.

As described above, in the apparatus and method for synchronizingfrequency in OFDM communication, the frequency offset estimationaccuracy is enhanced as well as the frequency offset estimation range isexpanded to

${{\hat{ɛ}} < \frac{N}{2D}},$using the two-step estimation method with fine and coarse modes, suchthat the carrier frequency synchronization is completely performed inthe digital domain.

Also, the hardware used in the two-step estimation method can be used inthe one-step estimation method using just one kind of training signal.

Still more, even though the initial phase rotation amount 2πεΔt existsin data symbol, the initial phase rotation amount 2πεΔt is estimatedwhen the channel is estimated such that the initial phase rotationamount can be compensated in the frequency domain equalizer.

Also, in the present invention, the phase rotation,

$\frac{{j2\pi}\left( {n_{d} - n_{f}} \right)}{N},$caused by the difference between the carrier frequency offsetcompensation point and the channel estimation point of the data symbolis estimated and compensated together with the phase rotation caused bythe residual frequency in the residual phase estimation part in thetracking mode, such that the carrier frequency can be completelysynchronized in the digital domain.

Furthermore, the estimation part and the frequency offset compensationmodule are shared by the residual phase tracking part in the trackingmode such that the overall implementation space of the frequencysynchronization apparatus can be reduced, leading to the increase ofsynchronization speed.

Since the frequency offset estimation and frequency synchronization isperformed in the digital domain, the frequency offset estimation andfrequency synchronization circuit can be separated from analog domainpart, resulting in reduction of overall manufacturing cost and highintegration of the circuit.

1. A frequency synchronization apparatus for an orthogonal frequencydivision multiplexing (OFDM) communication system, the frequencysynchronization apparatus comprising: a radio frequency (RF) receiverfor receiving an OFDM signal; an analog/digital (A/D) converterconnected to the RF receiver, the A/D converter converting the OFDMsignal into a digital signal; a frequency synchronizer connected to theA/D converter, the frequency synchronizer synchronizing a carrierfrequency; a Fast Fourier Transformer (FFT) connected to the frequencysynchronizer, the FFT performing fast Fourier transformation to symbolsfrom the frequency synchronizer; a channel estimator connected to theFFT, the channel estimator estimating a carrier channel; an equalizerconnected to the FFT and the channel estimator, the equalizer configuredfor equalizing a channel; a residual phase tracker connected to theequalizer, the residual phase tracker configured for tracking a residualphase; a demodulator connected to the residual phase tracker, thedemodulator configured for demodulating; and a controller connected tothe frequency synchronizer, the controller controlling the frequencysynchronizer, wherein if the received signal contains both short andlong training signals, the frequency synchronizer estimates thefrequency offset of the short training signal so as to compensate thelong training signal with the frequency offset of the short trainingsignal in a coarse mode, and re-estimates the frequency offset of thecompensated long training signal so as to re-compensate the longtraining signal in a fine mode.
 2. A frequency synchronization apparatusfor an orthogonal frequency division multiplexing (OFDM) communicationsystem, the frequency synchronization apparatus comprising: a radiofrequency (RF) receiver for receiving an OFDM signal; an analog/digital(A/D) converter connected to the RF receiver, the A/D converterconverting the OFDM signal into a digital signal; a frequencysynchronizer connected to the A/D converter, the frequency synchronizersynchronizing a carrier frequency; a Fast Fourier Transformer (FFT)connected to the frequency synchronizer, the FFT performing fast Fouriertransformation to symbols from the frequency synchronizer; a channelestimator connected to the FFT, the channel estimator estimating acarrier channel; an equalizer connected to the FFT and the channelestimator, the equalizer configured for equalizing a channel; a residualphase tracker connected to the equalizer, the residual phase trackerconfigured for tracking a residual phase; a demodulator connected to theresidual phase tracker, the demodulator configured for demodulating; anda controller connected to the frequency synchronizer, the controllercontrolling the frequency synchronizer, wherein if the receiver signalcontains one of both short and long training signals, the frequencysynchronizer estimates frequency offset of the training signal andcompensates the training signal and data symbol with the estimatedfrequency offset.
 3. The frequency synchronization apparatus of claim 1wherein frequency synchronizer compensates the data symbol with a sum ofthe frequency offsets estimated in the coarse and fine modes.
 4. Afrequency synchronization apparatus for an orthogonal frequency divisionmultiplexing (OFDM) communication system, the frequency synchronizationapparatus comprising: a radio frequency (RF) receiver for receiving anOFDM signal; an analog/digital (A/D) converter connected to the RFreceiver, the A/D converter converting the OFDM signal into a digitalsignal; a frequency synchronizer connected to the A/D converter, thefrequency synchronizer synchronizing a carrier frequency; a Fast FourierTransformer (FFT) connected to the frequency synchronizer, the FFTperforming fast Fourier transformation to symbols from the freauencysynchronizer; a channel estimator connected to the FFT, the channelestimator estimating a carrier channel; an equalizer connected to theFFT and the channel estimator, the equalizer confiqured for equalizing achannel; a residual phase tracker connected to the equalizer, theresidual phase tracker configured for tracking a residual phase; ademodulator connected to the residual phase tracker, the demodulatorconfigured for demodulating; and a controller connected to the frequencysynchronizer, the controller controlling the frequency synchronizer,wherein the frequency synchronizer comprises: an estimator forestimating frequency offset and residual phase of a received signal; afirst demultiplexer for selectively outputting the frequency offset andresidual phase estimated in the estimator; an adder for adding thefrequency offsets from the first demultiplexer; a frequency offsetcompensator for compensating the received signal and data symbol usingthe frequency offsets from the first demultiplexer and the adder; and asecond demultiplexer for selectively outputting a compensated signalfrom the frequency offset compensator.
 5. The frequency synchronizationapparatus of claim 4 wherein the estimator comprises: a shift registerfor delaying a sample of the training signal and outputting conjugatecomplex numbers of a predetermined training signal and a followingtraining signal at the same time; and a selective estimator forestimating frequency offset of a signal from the shift register andresidual phase of a signal from the residual phase tracker.
 6. Thefrequency synchronization apparatus of claim 5 wherein the selectiveestimator comprises: a first multiplier for multiplying the conjugatecomplex numbers of the signal from the shift register or the residualphase tracker; a first accumulator for accumulating samples obtained bymultiplication of the conjugate complex numbers at the first multiplier;a divider for generating an arctangent table address on the basis of aratio of a real part to an imaginary part of a value accumulated at thefirst accumulator; an arctangent table that stores arctangent valuessampled in a predetermined interval for outputting a correspondingarctangent value to the arctangent table address generated by thedivider; and a phase converter for converting the arctangent value intoa value of a corresponding region by referring to a sign of theaccumulated value at the first accumulator and outputting the value asan estimated frequency offset.
 7. The frequency synchronizationapparatus of claim 6 wherein the arctangent table is configured byclassifying the arctangent values into predetermined regions and storingthe values in a representative one of the regions as representativevalues.
 8. The frequency synchronization apparatus of claim 4 whereinthe frequency offset compensator comprises: a bit expander for samplingthe estimated frequency offset; a second accumulator for generating afirst log function table address by accumulating frequency offset ofeach sample obtained at the bit expander; a first region controller forconverting the first log function table address into a correspondingaddress value in a predetermined region by referring to a sign of valueat the bit expander; a first log function table for outputting apreviously stored log function value according to the address value fromthe first region controller; and a second multiplier for compensatingfrequency offset by multiplying the training signal or the data symbolby the log function value from the first log function table.
 9. Thefrequency synchronization apparatus of claim 8 wherein the first logfunction table is configured by dividing sine and cosine values intopredetermined regions and storing values in one of the regions asrepresentative values corresponding to the values in the other regions.10. The frequency synchronization apparatus of claim 9 wherein the firstregion controller outputs an address value resulting from a subtractionof a predetermined value from an output value and then shifts thepresent region to a next region if the output value is greater than thepredetermined value.
 11. The frequency synchronization apparatus ofclaim 9, wherein the first region controller performs a complementaryoperation with the output value of the second accumulator for obtaininga sine or cosine value in the representative regions.
 12. A freguencysynchronization apparatus for an orthogonal freguency divisionmultiplexing (OFDM) communication system, the freguency synchronizationapparatus comprising: a radio freauency (RF) receiver for receiving anOFDM signal; an analog/digital (A/D) converter connected to the RFreceiver, the A/D converter converting the OFDM signal into a digitalsignal; a freguency synchronizer connected to the A/D converter, thefreguency synchronizer synchronizing a carrier freguency; a Fast FourierTransformer (FFT) connected to the freguency synchronizer, the FFTperforming fast Fourier transformation to symbols from the freguencysynchronizer; a channel estimator connected to the FFT, the channelestimator estimating a carrier channel; an egualizer connected to theFFT and the channel estimator, the egualizer configured for egualizing achannel; a residual phase tracker connected to the equalizer, theresidual phase tracker configured for tracking a residual phase; ademodulator connected to the residual phase tracker, the demodulatorconfigured for demodulating; and a controller connected to the frequencysynchronizer, the controller controlling the frequency synchronizer,wherein the residual phase tracker comprises: a pilot extractor forextracting a pilot signal from a data symbol transformed by the FFT andsending the pilot signal to the frequency synchronizer; a residual phasecompensator for compensating the data symbol with the residual phase ofthe data symbol estimated at the frequency synchronizer.
 13. Thefrequency synchronization apparatus of claim 12 wherein the residualphase compensator comprises: a second region controller for outputting asecond log function table address corresponding to the residual phasevalue from the first demultiplexer; a second log function table foroutputting a previously stored log function value corresponding to thelog function table address from the second region controller; and athird multiplier for compensating the residual phase by multiplying thelog function value from the second log function table with thecompensated data symbol.
 14. The frequency synchronization apparatus ofclaim 13 wherein the second log function table is configured by dividingsine and cosine values into predetermined regions and values in one ofthe regions are stored as representative values corresponding to thevalues in the other regions.
 15. The frequency synchronization apparatusof claim 14 wherein the second region controller outputs an addressvalue resulting from a subtraction of a predetermined value from anoutput value and then shifts the present region to a next region if theoutput value is greater than the predetermined value.
 16. The frequencysynchronization apparatus of claim 15 wherein the second regioncontroller performs a complementary operation with the output value ofthe second accumulator for obtaining a sine or cosine value in therepresentative region.
 17. A frequency synchronization method for anorthogonal frequency division multiplexing (OFDM) communication systemcomprising: estimating a frequency offset of a training signal;compensating a frequency of the training signal with the estimatedfrequency offset; performing fast Fourier transformation on thefrequency; compensating a data symbol of an input signal with theestimated frequency offset; performing fast Fourier transformation onthe data symbol; compensating the data symbol with the estimated channelobtained by performing the fast Fourier transformation; tracking aresidual phase of the estimated data symbol; and compensating theresidual phase.
 18. The frequency synchronization method of claim 17wherein the estimating of the frequency offset, if the training signalhas short and long training signals, comprises: estimating the frequencyoffset using the short training signal; compensating the long trainingsignal with the estimated frequency offset of the short training in acoarse mode; estimating a frequency offset of the long compensatedtraining signal; and re-compensating the compensated long trainingsignal with the estimated frequency offset in a fine mode.
 19. Afrequency synchronization method of claim 18 wherein the data symbol iscompensated with a sum of the frequency offsets estimated in the fineand coarse modes.
 20. The frequency synchronization method of claim 18wherein the estimating of the frequency offset using the short trainingsignal, comprises: delaying a sample of the short training signal;outputting conjugate complex numbers of a present training signal and afollowing training signal at the same time; multiplying the conjugatecomplex numbers of the short training signal; accumulating values of thesamples obtained by the multiplying; first generating an arctangenttable address on the basis of a ratio of a real and imaginary parts ofthe accumulated values; referring to a sign of the accumulated value;converting an arctangent value stored in the first generated arctangenttable address of a generated arctangent table into a value in acorresponding region; and outputting the value as an estimated frequencyoffset.
 21. The frequency synchronization method of claim 20 whereincompensating the lone training signal with the estimated freguencyoffset of the short training in a coarse mode comprises: sampling theestimated frequency offset in a predetermined size; accumulating valuesof samples; generating a first log function table address on the basisof the accumulated value; referring to a sign of the accumulated value;converting a first log function table address into an address in acorresponding region; and first outputting a log function stored at theconverted address.
 22. The frequency synchronization method of claim 21wherein the first output log function value is multiplied with the longtraining signal.
 23. The frequency synchronization method of claim 20wherein the first generated arctangent table is configured byclassifying the arctangent values into predetermined regions and storingthe values in a representative one of the regions as representatives.24. The frequency synchronization method of claim 21 wherein the logfunction value is outputted after a complementary operation forobtaining a sine or cosine value in symmetrical regions.
 25. Thefrequency synchronization method of claim 21 wherein the first logfunction table is configured such that dividing sine and cosine valuesinto predetermined regions and values in one of the regions are storedas representative values corresponding to the values in the otherregions.
 26. The frequency synchronization method of claim 21 wherein anaddress value resulting from a subtraction of a predetermined value froman output value is outputted and then the present region is shifted to anext region if the output value is greater than the predetermined value.27. The frequency synchronization method of claim 21 wherein estimatinga freguency offset of the long compensated training signal comprises:delaying a sample of the compensated long training signal; outputtingconjugate complex numbers of a present long training signal and afollowing training signal at the same time; multiplying the conjugatecomplex numbers of the long training signal; accumulating values ofsamples obtained by multiplication of the conjugate complex numbers ofthe long training signal; second generating an arctangent table addresson the basis of a ratio of real and imaginary parts of the accumulatedvalue obtained by multiplication of the conjugate complex numbers of thelong training signal; referring to a sign of the accumulated value;converting the arctangent value stored in the second generatedarctangent table address of an arctangent table into a value in acorresponding region; and outputting the value as an estimated frequencyoffset.
 28. The frequency synchronization method of claim 27 wherein there-compensating comprises: sampling the estimated frequency offset in apredetermined size; accumulating values of samples; generating a logfunction table address on the basis of the accumulated value; referringto a sign of the accumulated value; converting a first log functiontable address of a first log function table into an address in acorresponding region; and second outputting a log function value storedat the converted address.
 29. The frequency synchronization method ofclaim 28 wherein the second output log function value is multiplied withthe long training signal.
 30. The frequency synchronization method ofclaim 27 wherein the arctangent table is configured classifying thearctangent values into predetermined regions and storing the values in arepresentative one of the regions as representatives.
 31. The frequencysynchronization method of claim 28 wherein the log function value isoutputted after a complementary operation for obtaining a sine or cosinevalue in symmetrical regions.
 32. The frequency synchronization methodof claim 28 wherein the first log function table is configured such thatdividing sine and cosine values into predetermined regions and values inone of the regions are stored as representative values corresponding tothe values in the other regions.
 33. The frequency synchronizationmethod of claim 28 wherein an address value resulting from a subtractionof a predetermined value from an output value is outputted and then thepresent region is shifted to a next region if the output value isgreater than the predetermined value.
 34. The frequency synchronizationmethod of claim 17 wherein tracking a residual phase comprises:extracting a pilot signal from the compensated data symbol; performing aconjugate complex number multiplication; accumulating values of samplesobtained by the complex number multiplication; generating an aretangenttable address on the basis of a ratio of real and imaginary parts of theaccumulated value; referring to a sign of the accumulated value;converting the arctangent value stored in the generated arctangent tableaddress of an arctangent table into a value in a corresponding region;outputting the value as an estimated residual phase; generating a secondlog function table address according to the estimated residual phase;outputting a log function value corresponding to the second log functiontable address of a second log function table; and multiplying the logfunction value with the data symbol.
 35. The frequency synchronizationmethod of claim 34 further comprising classifying the arctangent valuesinto predetermined regions and storing the values in a representativeone of the regions as representative values.
 36. The frequencysynchronization method of claim 34 the second log function table furthercomprising dividing sine and cosine values into predetermined regionsand storing values in one of the regions as representative valuescorresponding to the values in the other regions.
 37. The frequencysynchronization method of claim 34 further comprising outputting anaddress value resulting from a subtraction of a predetermined value froman output value and shifting the present region to a next region if theoutput value is greater than the predetermined value.
 38. The frequencysynchronization method of claim 34 further comprising outputting sineand cosine values after performing a complementary operation with thelog function value for obtaining sine or cosine value in symmetricalregions.